| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 14.0.564...000.1 |
$x^{14} + 3 x^{12} - 10 x^{11} + 20 x^{10} + 10 x^{9} + 73 x^{8} - 6 x^{7} + 41 x^{6} + 234 x^{5} + 64 x^{4} + 186 x^{3} + 403 x^{2} + 156 x + 45$ |
$14$ |
[0,7] |
$-\,2^{14}\cdot 5^{6}\cdot 7^{6}\cdot 37^{4}$ |
$4$ |
$25.7531927709$ |
$131.38077938391916$ |
|
|
? |
$C_7^2:(C_6\times S_3)$ (as 14T37) |
trivial |
$4$ |
$6$ |
$108233.425881$ |
| 14.0.193...923.1 |
$x^{14} - 14 x^{11} - 7 x^{10} + 42 x^{9} + 217 x^{8} - 106 x^{7} - 539 x^{6} - 294 x^{5} + 686 x^{4} + 595 x^{3} - 63 x^{2} - 105 x + 19$ |
$14$ |
[0,7] |
$-\,3^{7}\cdot 7^{14}\cdot 19^{4}$ |
$3$ |
$28.1200985948$ |
|
|
|
? |
$C_7^2:(C_6\times S_3)$ (as 14T37) |
trivial |
$6$ |
$6$ |
$178819.961267$ |
| 14.0.380...311.1 |
$x^{14} - 28 x^{11} - 28 x^{9} + 203 x^{8} + 2 x^{7} + 392 x^{6} - 98 x^{5} + 168 x^{4} - 98 x^{3} + 364 x^{2} + 7 x + 1$ |
$14$ |
[0,7] |
$-\,7^{12}\cdot 31^{7}$ |
$2$ |
$29.51553063885384$ |
$49.134415769117915$ |
|
|
? |
$C_7^2:(C_6\times S_3)$ (as 14T37) |
$[3]$ |
$2$ |
$6$ |
$46928.44545584693$ |
| 14.0.230...503.1 |
$x^{14} - 28 x^{11} + 14 x^{10} + 203 x^{8} - 183 x^{7} + 49 x^{6} - 98 x^{5} - 133 x^{4} + 91 x^{3} + 294 x^{2} - 35 x + 48$ |
$14$ |
[0,7] |
$-\,7^{14}\cdot 23^{7}$ |
$2$ |
$33.57082066318904$ |
$45.82079975673942$ |
|
|
? |
$C_7^2:(C_6\times S_3)$ (as 14T37) |
$[3]$ |
$2$ |
$6$ |
$150402.99786834148$ |
| 14.2.336...648.1 |
$x^{14} - 28 x^{11} + 14 x^{10} + 84 x^{9} + 182 x^{8} - 162 x^{7} - 1127 x^{6} + 784 x^{5} + 1190 x^{4} - 350 x^{3} - 336 x^{2} + 280 x + 252$ |
$14$ |
[2,6] |
$2^{8}\cdot 7^{12}\cdot 37^{7}$ |
$3$ |
$47.9167938087$ |
$85.21037475751343$ |
|
|
|
$C_7^2:(C_6\times S_3)$ (as 14T37) |
trivial |
$2$ |
$7$ |
$9972446.44061$ |
| 14.2.164...752.1 |
$x^{14} - 28 x^{11} + 14 x^{10} + 140 x^{9} + 168 x^{8} - 128 x^{7} - 1911 x^{6} + 1372 x^{5} + 3752 x^{4} - 1484 x^{3} - 2296 x^{2} + 1120 x + 1008$ |
$14$ |
[2,6] |
$2^{8}\cdot 7^{14}\cdot 37^{7}$ |
$3$ |
$63.2726526754$ |
|
|
|
|
$C_7^2:(C_6\times S_3)$ (as 14T37) |
trivial |
$2$ |
$7$ |
$61458222.2384$ |
| 14.14.103...000.1 |
$x^{14} - 210 x^{12} - 420 x^{11} + 13615 x^{10} + 49420 x^{9} - 227640 x^{8} - 1102840 x^{7} + 537775 x^{6} + 6881000 x^{5} + 4518150 x^{4} - 11484900 x^{3} - 14154175 x^{2} - 3350900 x - 207900$ |
$14$ |
[14,0] |
$2^{16}\cdot 5^{12}\cdot 7^{14}\cdot 37^{7}$ |
$4$ |
$373.551366436$ |
|
|
|
|
$C_7^2:(C_6\times S_3)$ (as 14T37) |
trivial |
$2$ |
$13$ |
$94986945469500$ |
| 14.14.983...272.1 |
$x^{14} - 546 x^{12} - 1820 x^{11} + 94367 x^{10} + 567476 x^{9} - 4735640 x^{8} - 37791624 x^{7} + 74520719 x^{6} + 960908312 x^{5} + 178767862 x^{4} - 10031125468 x^{3} - 11527474959 x^{2} + 33962524596 x + 53095268772$ |
$14$ |
[14,0] |
$2^{16}\cdot 7^{14}\cdot 13^{12}\cdot 37^{7}$ |
$4$ |
$847.308904499$ |
|
|
|
|
$C_7^2:(C_6\times S_3)$ (as 14T37) |
trivial |
$2$ |
$13$ |
$29462583765900000$ |
